Regularity of weakly harmonic maps from a Finsler surface into an \(n\)-sphere (Q657370)

Harmonic maps between Riemannian manifolds are very important tools in differential geometry. They are defined as the critical points of the energy functionals. Finsler manifolds are just Riemannian manifolds with metrics without the quadratic restriction. In this paper, the authors study the theory of harmonic maps on Finsler surfaces. They obtain the conformal invariance of Finsler harmonic maps from surfaces by using Berwald frames on surfaces. Finally, as an application, the authors obtain a regularity result of a weakly Finsler harmonic map on a Finsler surface \(M\), generalizing a theorem of \textit{F. Hélein} [C. R. Acad. Sci., Paris, Sér. I 311, No. 9, 519--524 (1990; Zbl 0728.35014)] for the case of a Riemannian surface \(M\).